Chapter SIX. Dealing with Unequal Variance Around the Regression Line

Summary

We demonstrate that the ordinary least squares estimator is unbiased even with unequal variance. The effect of unequal variance on the derivation of the variance of ordinary regression estimators is pointed out. The use of the empirical (robust or Huber) estimator is introduced as a solution to obtaining correct standard errors. Empirical estimator obtained by PROC MIXED. Examples of applying empirical option to regressions of glycosylated hemoglobin on age and of systolic blood pressure on age, BMI and gender.

The functional transformation approach is introduced as one approach to unequal variance. An approximate formula is given for choosing the transformation. Example of regressing inverse of GHb on diabetes duration. Log of outcome on log of predictor regression is discussed and interpreted as elasticity. Example of the cost of medical care on gender and BMI.

Weighted least squares derived from linear transformation to obtain efficient estimators. Unbiasedness of weighted least squares estimators is demonstrated. Model based and empirical standard errors are derived. Weighted least squares are applied by PROC REG and PROC MIXED to regression of GHb on diabetes duration.